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Question: Let I be a monomial ideal in K[t1,...,tq] and X = V(I) ⊂ Aq K the associated monomial variety. If K is infinite, prove that X is irreducible if and only if X = V (ti1 ,...,tir )? 0 Let K be an infinite field. Prove:
(a) Aq K is an irreducible variety,
(b) any two non-empty open sets of Aq K intersect,
(c) any non-empty open set of AqK is dense,
(d) (K∗)q is an open set of AqK,
(e) (K∗)q is not an affine variety.
A 1976 study of women smokers over 30 years of age who delivered premature babies (fewer than 260 days of gestation) reported an infant survival percentage of 72%. Suppose researchers would like to estimate the current survival proportion. Using the..
Investigate the presence of limit cycles both analytically and numberically and investigate the presence of homoclinic/heteroclinic orbits and global bifurcations numerically.
Francisco and Ryan are stuck simplifying radical expressions. Francisco has simplified to . Ryan has simplified to . Using full sentences, describe how to fully simplify Francisco and Ryan's expressions. Describe if Francisco and Ryan started with..
What are the inputs for this algorithm? Is the algorithm correct? Comment on the algorithm's clarity.
AIRLINE SAFETY In an attempt to study the leading causes of airline crashes, the following data were compiled from records of airline crashes from 1959 to 1994.
In 2004, these figures had risen to 77.8 and 83.7, respectively. In both cases, the increase in life expectancy has been linear. Using these assumptions and the data given, and the maximum life expectancy for humans. Source: Science.
Suppose that on Monday there are 295 cars at the airport (or rented from there), 55 cars at the east side office, and 150 cars at the west side office.
the company policy for customer service representatives gives time off for positive reviews. if in the first 20 calls a
a weather balloon is rising vertically. after T hours, its distance above the ground measured in kilometers is given by the formula s(t)=8t-t2. determine the average velocity of weather balloon from t=2h to t=5h. determine its velocity at t=3h.
A merchant has coffee with $20 a pound that she wishes to mix with 70 pounds of coffee $90 a pound to get a mixture that is worth $30 a pound. How many pounds (lb) of the $20 coffee should be used?
in a study to compare the effects on physical performance of different types of food consumed prior to exercise an
A constant force F= -3i + 8j +10k moves an object along a straight line from point (-6, -5, -4) to point (-3, 1, -6). Find the work done if the distance is measured in meters and the magnitude of the force is measured in Newtons.
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